## Elements of Geometry |

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### Common terms and phrases

acute adjacent altitude base bisect called centre chord circle circumference circumscribed coincide common Cons construct contained COROLLARY describe diagonals diameter difference direction divided Draw equal distances equal respectively equiangular equilateral equivalent erected extremities fall figure formed four given greater Hence homologous sides hypotenuse included inscribed intercept intersect isosceles joining less Let A B limit line A B line drawn mean measured meet middle point multiplied number of sides one-half opposite sides parallelogram perimeter perpendicular plane position PROBLEM proportional prove Q. E. D. PROPOSITION quadrilateral quantities radii radius equal ratio rect rectangles regular polygon right angles segment Show similar similar polygons square straight line Substitute subtend surface symmetrical Take taken tangent THEOREM triangle variable vertex vertices

### Popular passages

Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.

Page 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...

Page 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.

Page 202 - In any proportion, the product of the means is equal to the product of the extremes.

Page 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.

Page 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.

Page 146 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.